Polyomino squares

In a thread appeared in Nov. 2009 in the newsgroup it.hobby.enigmi, we searched for ways to cover squares with polyominoes. Here I collect some results on the 3 following problems.

	For each kind of polyomino (say, for the pentominoes) we searched for the largest square that can be covered by that polyominoes. Livio Zucca found an incredible 210×210 square made of 4410 decominoes. See the results!
	We looked for square that can be formed by complete series of polyominoes (possibly disregarding those with holes). See the results!
	I have also searched for square frames that can be filled with complete series of polyominoes. See the results!

Clearly, it is possible to extend the search in several directions....